As my avatar shows I like little smokey. He was my first pet I had and used all the time. But I just discovered hes uncommon. Could I go engineer a bunch more till I got a rare? Or is he just forever flagged as uncommon?

If he is stuck, I wish they could do something about that. Maybe a special battle that would up the rarity of a pet or whatever.

Only captured pets boast variable Rarity. Those learned from items or obtained by other traditional means have a predefined Rarity based on how they were obtained and how numerous they are. The developers have hinted that they are considering ways of making our favorite pets stronger, but other than this passing hint there has been no word on such a feature.